12n^2=-24n+128

Solution for 12n^2=-24n+128 equation:

12n^2=-24n+128

We move all terms to the left:

12n^2-(-24n+128)=0

We get rid of parentheses

12n^2+24n-128=0

a = 12; b = 24; c = -128;
Δ = b2-4ac
Δ = 242-4·12·(-128)
Δ = 6720
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6720}=\sqrt{64*105}=\sqrt{64}*\sqrt{105}=8\sqrt{105}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{105}}{2*12}=\frac{-24-8\sqrt{105}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{105}}{2*12}=\frac{-24+8\sqrt{105}}{24}
$